Substructuring and poroelastic modelling of the intervertebral disc

Area of Science:

• Biomechanics
• Computational Biology
• Materials Science

Background:

• Finite element analysis (FEA) is crucial for simulating biological tissue behavior.
• Poroelasticity accurately models fluid-saturated porous media, common in biological tissues.
• Simulating time-dependent responses of complex structures like intervertebral discs requires efficient computational methods.

Purpose of the Study:

• To introduce and validate a substructure technique for predicting the time-dependent poroelastic response of biological tissues.
• To assess the accuracy and efficiency of the substructure method compared to a full finite element model.
• To evaluate the technique's applicability to a specific musculoskeletal structure, the L(5)-S(1) intervertebral disc.

Main Methods:

• Developed a substructure technique within a finite element framework for poroelasticity.
• Calculated the sub-structured poroelastic matrix and obtained transient responses using exponential fitting.
• Applied the method to a 3D reconstructed L(5)-S(1) intervertebral disc from a scoliotic spine, reducing degrees of freedom from 10,000 to 40.

Main Results:

• The substructure model showed less than 10% discrepancy in displacement compared to the full model during initial time steps.
• Achieved exact quasi-static solutions after pressure relaxation.
• Successfully preserved couplings between vertical and transversal displacements despite a significant reduction in degrees of freedom.

Conclusions:

• The substructuring technique is highly efficient for reducing the computational size of numerical models.
• The method accurately respects the time-dependent behavior of poroelastic structures.
• Substructure techniques hold significant potential for large-scale modeling of musculoskeletal structures.